Enhancing the Spalart–Allmaras Model for Transonic Airfoils Using Field Inversion/Machine Learning

Reynolds-averaged Navier–Stokes (RANS) simulations are widely used in industrial design due to their favorable balance between accuracy, computational cost, and turnaround time. However, RANS models often struggle to predict complex flows involving separation or strong adverse pressure gradients. In transonic flows over airfoils, even attached flow regimes remain challenging, primarily due to the misprediction of the shock location. Since the shock position strongly affects the wall-pressure distribution, these inaccuracies propagate to uncertainties in cruise performance predictions, such as lift and drag. To address this limitation, the present study employs a combined field inversion and machine learning framework to enhance the Spalart–Allmaras turbulence model. In this approach, wall-pressure data from experimental databases (OAT15A and RAE2822 airfoils) are first assimilated via field inversion to extract spatially dependent corrective fields. An artificial neural network is then trained to reconstruct this correction by mapping it to a set of local, Galilean-invariant input features. The results demonstrate a substantial improvement in pressure coefficient predictions for both in-sample and out-of-sample cases, without degrading the friction coefficient of a zero-pressure-gradient flat-plate boundary layer. We also highlight the potential of machine learning to enhance RANS modeling for complex three-dimensional transonic aircraft configurations.